Find the range of each of the following functions:
(i) f{x) = 2 - 3x, x ∈ R,x>0
(ii) f(x) = x2 + 2, x is a real number
(iii) f(x) = x, x is a real number.
(i) Given f(x) = 2 - 3x, x ∈ R,x > 0
For x > 0, f(x) = 2 – 3x < 2
∴ Range of f = (-∞, 2)
(ii) Given f(x) = x2 + 2, x ∈ R
For x ∈ R, f(x) = x2 + 2 ≥ 2
Range of f = [2, ∞)
(iii) Given f(x) = x, x∈ R For r∈ E, f(x) = x ∈ R
Range of f = R